Handle non-semi-explicit mass matrices

[baggepinnen]

On latest master

using ModelingToolkit, OrdinaryDiffEq

@parameters t M[1:2,1:2] Dq[1:2,1:2] 
@variables q[1:2](t)
@derivatives D'~t


arm_eqs   = M*D.(D.(q)) + Dq*D.(q) .~ 0
armsys    = ODESystem(arm_eqs, name=:arm)


julia> armsys    = ODESystem(arm_eqs, name=:arm)
ERROR: MethodError: Cannot `convert` an object of type 
  typeof(+) to an object of type 
  Variable
Closest candidates are:
  convert(::Type{Variable}, ::Operation) at /home/fredrikb/.julia/dev/ModelingToolkit/src/ModelingToolkit.jl:81
  convert(::Type{T}, ::Intervals.Interval{T,L,R} where R<:Intervals.Bound where L<:Intervals.Bound) where T at /home/fredrikb/.julia/packages/Intervals/T6hJb/src/interval.jl:194
  convert(::Type{T}, ::Intervals.AnchoredInterval{P,T,L,R} where R<:Intervals.Bounded where L<:Intervals.Bounded) where {P, T} at /home/fredrikb/.julia/packages/Intervals/T6hJb/src/anchoredinterval.jl:177
  ...
Stacktrace:
 [1] setindex!(::OrderedCollections.OrderedDict{Variable,Nothing}, ::Nothing, ::Function) at /home/fredrikb/.julia/packages/OrderedCollections/BvIBz/src/ordered_dict.jl:287
 [2] push!(::OrderedCollections.OrderedSet{Variable}, ::Function) at /home/fredrikb/.julia/packages/OrderedCollections/BvIBz/src/ordered_set.jl:25
 [3] ODESystem(::Array{Equation,1}, ::Nothing; kwargs::Base.Iterators.Pairs{Symbol,Symbol,Tuple{Symbol},NamedTuple{(:name,),Tuple{Symbol}}}) at /home/fredrikb/.julia/dev/ModelingToolkit/src/systems/diffeqs/odesystem.jl:122
 [4] top-level scope at none:1

[baggepinnen]

I think the error comes from iv_from_nested_derivative(eq.lhs) returning an operator rather than the independent variable, maybe because I wrote the expression with the mass matrix rather than multiplying everything by the inverse mass matrix?

I have to write the expression like this for it to work

arm_eqs   = simplify.(D.(D.(q)) .~ -M\Dq*D.(q))

but I'm not sure how well that scales to a larger M than 2 by 2

[ChrisRackauckas]

Yeah right now it won't fully simplify the mass matrix, but this is a good test equation for higher order DAEs.